Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_pH 9 6.563471
beta0_pH 14 3.075230
beta3_black 2 1.686569
beta0_black 2 1.625300
mu_beta0_pH 2 1.590838
beta1_black 13 1.408187
beta1_pH 20 1.369633
beta1_pelagic 7 1.347945
beta3_yellow 2 1.331617
beta2_yellow 7 1.295234
beta0_pelagic 6 1.294714
parameter n badRhat_avg
beta2_pelagic 4 1.271116
beta2_black 3 1.255569
beta2_pH 16 1.254890
tau_beta0_pH 1 1.188711
beta0_yellow 4 1.188042
beta1_yellow 4 1.185026
beta3_pelagic 2 1.184457
tau_beta0_yellow 2 1.150886
beta4_yellow 1 1.150232
tau_beta0_pelagic 1 1.134166
beta4_pelagic 1 1.115866
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
beta0_pelagic 0 1 0 1 0 0 0 1 0 0 1 1 0 0 1 0
beta0_pH 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1
beta0_yellow 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1
beta1_black 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1
beta1_pelagic 1 1 0 1 0 0 0 0 0 0 1 1 0 0 1 1
beta1_pH 1 1 1 0 1 0 1 1 1 0 1 1 1 1 0 1
beta1_yellow 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1
beta2_black 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0
beta2_pelagic 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0
beta2_pH 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1
beta2_yellow 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1
beta3_black 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
beta3_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
beta3_pH 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 0
beta3_yellow 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1
beta4_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta4_yellow 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.133 0.073 -0.271 -0.136 0.020
mu_bc_H[2] -0.096 0.044 -0.172 -0.099 0.001
mu_bc_H[3] -0.431 0.071 -0.565 -0.432 -0.290
mu_bc_H[4] -0.992 0.188 -1.372 -0.992 -0.620
mu_bc_H[5] 0.955 0.981 -0.130 0.752 3.328
mu_bc_H[6] -2.182 0.327 -2.783 -2.192 -1.510
mu_bc_H[7] -0.463 0.112 -0.690 -0.461 -0.245
mu_bc_H[8] 0.228 0.355 -0.355 0.194 1.037
mu_bc_H[9] -0.294 0.134 -0.556 -0.296 -0.023
mu_bc_H[10] -0.111 0.069 -0.243 -0.113 0.033
mu_bc_H[11] -0.125 0.039 -0.200 -0.125 -0.049
mu_bc_H[12] -0.256 0.104 -0.487 -0.249 -0.067
mu_bc_H[13] -0.137 0.078 -0.289 -0.137 0.022
mu_bc_H[14] -0.298 0.099 -0.498 -0.297 -0.108
mu_bc_H[15] -0.344 0.051 -0.439 -0.345 -0.239
mu_bc_H[16] -0.258 0.371 -0.904 -0.282 0.544
mu_bc_R[1] 1.310 0.144 1.042 1.312 1.599
mu_bc_R[2] 1.449 0.095 1.249 1.452 1.626
mu_bc_R[3] 1.392 0.142 1.120 1.391 1.676
mu_bc_R[4] 0.917 0.202 0.480 0.926 1.285
mu_bc_R[5] 1.145 0.467 0.244 1.140 2.043
mu_bc_R[6] -1.586 0.424 -2.407 -1.596 -0.746
mu_bc_R[7] 0.266 0.192 -0.104 0.259 0.652
mu_bc_R[8] 0.559 0.201 0.154 0.568 0.933
mu_bc_R[9] 0.338 0.207 -0.115 0.353 0.700
mu_bc_R[10] 1.322 0.138 1.035 1.327 1.574
mu_bc_R[11] 1.047 0.098 0.853 1.047 1.234
mu_bc_R[12] 0.827 0.211 0.391 0.832 1.217
mu_bc_R[13] 1.033 0.105 0.825 1.035 1.235
mu_bc_R[14] 0.904 0.142 0.627 0.903 1.182
mu_bc_R[15] 0.773 0.112 0.556 0.776 0.994
mu_bc_R[16] 1.089 0.129 0.827 1.090 1.336
tau_pH[1] 5.241 0.453 4.421 5.221 6.168
tau_pH[2] 1.877 0.891 0.584 2.267 3.088
tau_pH[3] 2.436 0.384 1.854 2.353 3.293
beta0_pH[1,1] 0.519 0.180 0.161 0.525 0.858
beta0_pH[2,1] 1.324 0.189 0.920 1.337 1.676
beta0_pH[3,1] 1.398 0.234 0.940 1.421 1.759
beta0_pH[4,1] 1.584 0.199 1.170 1.591 1.940
beta0_pH[5,1] -0.859 0.295 -1.514 -0.839 -0.342
beta0_pH[6,1] -0.606 0.396 -1.598 -0.546 -0.010
beta0_pH[7,1] -0.152 0.585 -1.163 -0.256 0.902
beta0_pH[8,1] -0.639 0.268 -1.265 -0.616 -0.193
beta0_pH[9,1] -0.642 0.277 -1.226 -0.618 -0.164
beta0_pH[10,1] 0.188 0.200 -0.203 0.189 0.585
beta0_pH[11,1] -0.061 0.174 -0.392 -0.057 0.281
beta0_pH[12,1] 0.499 0.187 0.141 0.497 0.859
beta0_pH[13,1] 0.004 0.145 -0.285 0.003 0.284
beta0_pH[14,1] -0.308 0.168 -0.644 -0.307 0.021
beta0_pH[15,1] -0.004 0.173 -0.340 -0.006 0.330
beta0_pH[16,1] -0.446 0.341 -1.212 -0.394 0.090
beta0_pH[1,2] 2.749 0.253 2.216 2.754 3.235
beta0_pH[2,2] 2.826 0.249 2.158 2.844 3.270
beta0_pH[3,2] 2.697 0.418 1.944 2.647 3.471
beta0_pH[4,2] 2.767 0.346 1.968 2.829 3.316
beta0_pH[5,2] 4.636 1.570 2.535 4.330 8.782
beta0_pH[6,2] 2.958 0.395 2.281 2.929 3.762
beta0_pH[7,2] 1.951 0.251 1.454 1.947 2.500
beta0_pH[8,2] 2.840 0.262 2.352 2.843 3.334
beta0_pH[9,2] 2.988 0.824 1.522 3.174 4.184
beta0_pH[10,2] 3.672 0.322 3.083 3.694 4.202
beta0_pH[11,2] -4.827 0.412 -5.653 -4.842 -3.905
beta0_pH[12,2] -4.764 0.564 -5.885 -4.768 -3.609
beta0_pH[13,2] -2.782 2.548 -5.244 -4.312 1.164
beta0_pH[14,2] -5.797 0.549 -6.920 -5.767 -4.801
beta0_pH[15,2] -2.561 2.366 -4.790 -4.002 1.137
beta0_pH[16,2] -4.893 0.518 -5.997 -4.871 -3.845
beta0_pH[1,3] 0.645 0.615 -0.872 0.803 1.443
beta0_pH[2,3] 1.937 0.494 0.375 2.075 2.449
beta0_pH[3,3] 2.285 0.327 1.486 2.369 2.732
beta0_pH[4,3] 2.757 0.393 1.644 2.851 3.200
beta0_pH[5,3] 1.239 1.685 -1.332 0.971 5.315
beta0_pH[6,3] -0.598 1.034 -2.591 -0.719 1.457
beta0_pH[7,3] -2.000 0.558 -3.237 -1.964 -1.016
beta0_pH[8,3] 0.281 0.191 -0.098 0.285 0.654
beta0_pH[9,3] -0.760 0.613 -2.389 -0.600 -0.006
beta0_pH[10,3] 0.145 0.927 -2.149 0.501 1.198
beta0_pH[11,3] -0.162 0.299 -0.719 -0.167 0.426
beta0_pH[12,3] -0.885 0.335 -1.633 -0.862 -0.297
beta0_pH[13,3] -0.146 0.301 -0.739 -0.142 0.425
beta0_pH[14,3] -0.294 0.263 -0.808 -0.297 0.222
beta0_pH[15,3] -0.746 0.281 -1.313 -0.749 -0.167
beta0_pH[16,3] -0.425 0.269 -0.941 -0.425 0.111
beta1_pH[1,1] 3.109 0.323 2.516 3.087 3.812
beta1_pH[2,1] 2.204 0.284 1.715 2.178 2.816
beta1_pH[3,1] 2.062 0.467 1.500 1.994 2.911
beta1_pH[4,1] 2.370 0.301 1.853 2.352 3.047
beta1_pH[5,1] 2.324 0.362 1.713 2.293 3.174
beta1_pH[6,1] 3.739 1.038 2.283 3.542 6.340
beta1_pH[7,1] 2.359 1.030 0.517 2.334 4.692
beta1_pH[8,1] 3.922 0.919 2.580 3.728 6.183
beta1_pH[9,1] 2.318 0.369 1.723 2.276 3.199
beta1_pH[10,1] 2.436 0.279 1.898 2.430 3.013
beta1_pH[11,1] 3.234 0.217 2.819 3.231 3.668
beta1_pH[12,1] 2.535 0.219 2.118 2.534 2.968
beta1_pH[13,1] 2.978 0.215 2.582 2.971 3.421
beta1_pH[14,1] 3.416 0.219 2.991 3.413 3.856
beta1_pH[15,1] 2.505 0.219 2.078 2.506 2.930
beta1_pH[16,1] 4.107 0.627 3.182 4.027 5.472
beta1_pH[1,2] 3.113 15.005 0.000 0.316 30.032
beta1_pH[2,2] 1.732 5.657 0.000 0.209 12.189
beta1_pH[3,2] 0.763 0.629 0.000 0.946 1.727
beta1_pH[4,2] 2.326 8.154 0.000 0.580 23.028
beta1_pH[5,2] 6.475 15.645 0.000 0.570 64.054
beta1_pH[6,2] 1.185 3.554 0.000 0.861 3.407
beta1_pH[7,2] 6.134 19.444 0.000 0.286 79.500
beta1_pH[8,2] 11.345 29.526 0.000 0.287 115.709
beta1_pH[9,2] 3.691 13.937 0.000 0.802 62.059
beta1_pH[10,2] 7.975 16.006 0.000 1.662 58.298
beta1_pH[11,2] 6.680 0.437 5.731 6.684 7.569
beta1_pH[12,2] 6.463 0.652 5.202 6.448 7.831
beta1_pH[13,2] 7.190 2.742 4.440 6.972 10.736
beta1_pH[14,2] 7.421 0.572 6.333 7.409 8.556
beta1_pH[15,2] 6.835 1.498 4.063 6.743 10.300
beta1_pH[16,2] 7.445 0.555 6.261 7.455 8.518
beta1_pH[1,3] 2.874 1.233 1.490 2.488 6.197
beta1_pH[2,3] 1.098 6.137 0.000 0.232 4.713
beta1_pH[3,3] 0.415 1.070 0.000 0.123 1.478
beta1_pH[4,3] 0.850 4.208 0.000 0.107 4.858
beta1_pH[5,3] 4.561 16.330 1.511 2.967 8.634
beta1_pH[6,3] 2.616 1.193 1.133 2.498 4.821
beta1_pH[7,3] 2.849 0.563 1.861 2.795 4.103
beta1_pH[8,3] 2.770 0.345 2.133 2.752 3.464
beta1_pH[9,3] 2.820 0.629 1.949 2.681 4.500
beta1_pH[10,3] 3.241 0.996 2.051 2.883 5.734
beta1_pH[11,3] 2.735 0.360 2.033 2.728 3.451
beta1_pH[12,3] 4.142 0.417 3.341 4.128 5.011
beta1_pH[13,3] 1.871 0.360 1.178 1.862 2.608
beta1_pH[14,3] 2.567 0.340 1.905 2.573 3.226
beta1_pH[15,3] 2.174 0.408 1.417 2.152 2.982
beta1_pH[16,3] 1.870 0.315 1.258 1.870 2.482
beta2_pH[1,1] 0.473 0.126 0.294 0.457 0.753
beta2_pH[2,1] 0.553 0.259 0.240 0.504 1.164
beta2_pH[3,1] 0.610 0.411 0.191 0.530 1.629
beta2_pH[4,1] 0.480 0.239 0.236 0.445 0.895
beta2_pH[5,1] 1.207 1.076 0.216 0.892 3.901
beta2_pH[6,1] 0.194 0.067 0.095 0.184 0.352
beta2_pH[7,1] -0.238 1.100 -3.649 0.026 0.713
beta2_pH[8,1] 0.249 0.086 0.132 0.233 0.467
beta2_pH[9,1] 0.434 0.226 0.184 0.398 0.885
beta2_pH[10,1] 0.592 0.285 0.289 0.530 1.294
beta2_pH[11,1] 0.793 0.211 0.483 0.763 1.280
beta2_pH[12,1] 1.371 0.523 0.746 1.266 2.619
beta2_pH[13,1] 0.730 0.225 0.410 0.696 1.249
beta2_pH[14,1] 0.840 0.214 0.533 0.806 1.333
beta2_pH[15,1] 0.814 0.282 0.430 0.761 1.506
beta2_pH[16,1] 0.370 0.168 0.177 0.321 0.827
beta2_pH[1,2] -3.523 9.498 -22.189 -3.757 17.412
beta2_pH[2,2] -4.002 9.208 -22.066 -4.348 16.979
beta2_pH[3,2] -4.528 9.163 -22.696 -4.673 17.321
beta2_pH[4,2] -4.514 9.164 -22.018 -4.741 18.420
beta2_pH[5,2] -5.992 9.372 -22.731 -6.640 15.471
beta2_pH[6,2] -6.224 9.350 -22.984 -6.808 15.489
beta2_pH[7,2] -6.398 9.368 -23.442 -7.051 15.215
beta2_pH[8,2] -6.178 9.383 -23.242 -6.665 15.214
beta2_pH[9,2] -6.347 9.245 -23.204 -6.902 15.401
beta2_pH[10,2] -6.489 9.380 -22.819 -7.153 16.022
beta2_pH[11,2] -7.260 3.226 -15.105 -6.508 -3.045
beta2_pH[12,2] -5.789 3.727 -14.623 -5.351 -0.704
beta2_pH[13,2] -5.925 3.539 -14.706 -5.298 -1.560
beta2_pH[14,2] -6.446 3.101 -14.460 -6.055 -2.156
beta2_pH[15,2] -7.473 3.357 -15.452 -6.831 -2.538
beta2_pH[16,2] -7.838 3.321 -16.336 -7.114 -3.333
beta2_pH[1,3] 3.695 5.306 0.128 0.772 18.612
beta2_pH[2,3] 3.211 6.427 -7.952 1.744 18.887
beta2_pH[3,3] 2.376 6.745 -8.423 0.828 19.099
beta2_pH[4,3] 2.919 6.632 -8.183 1.603 18.897
beta2_pH[5,3] 7.784 6.091 0.248 6.540 23.232
beta2_pH[6,3] 7.743 6.128 0.131 6.476 22.533
beta2_pH[7,3] 7.641 6.094 0.600 6.298 22.264
beta2_pH[8,3] 8.845 5.622 0.979 7.950 22.629
beta2_pH[9,3] 7.335 6.327 0.339 6.102 22.705
beta2_pH[10,3] 6.660 6.528 0.339 5.030 22.567
beta2_pH[11,3] -1.990 1.495 -5.982 -1.603 -0.624
beta2_pH[12,3] -2.077 1.241 -5.144 -1.789 -0.957
beta2_pH[13,3] -2.425 1.711 -6.966 -1.932 -0.817
beta2_pH[14,3] -2.435 1.705 -7.371 -1.905 -0.941
beta2_pH[15,3] -2.527 1.788 -7.367 -2.009 -0.981
beta2_pH[16,3] -2.610 1.887 -7.721 -2.023 -0.882
beta3_pH[1,1] 35.815 0.805 34.296 35.791 37.473
beta3_pH[2,1] 33.401 1.172 31.364 33.327 35.972
beta3_pH[3,1] 33.862 1.263 31.785 33.770 36.548
beta3_pH[4,1] 33.879 1.171 31.733 33.823 36.428
beta3_pH[5,1] 28.044 1.380 26.496 27.639 31.852
beta3_pH[6,1] 38.742 3.088 33.229 38.548 44.997
beta3_pH[7,1] 29.615 8.789 18.363 27.987 45.426
beta3_pH[8,1] 39.876 2.049 36.260 39.680 44.834
beta3_pH[9,1] 30.654 1.475 28.010 30.521 33.969
beta3_pH[10,1] 32.575 0.887 30.935 32.519 34.459
beta3_pH[11,1] 30.410 0.482 29.523 30.396 31.345
beta3_pH[12,1] 30.179 0.408 29.331 30.181 30.962
beta3_pH[13,1] 33.192 0.591 32.055 33.174 34.417
beta3_pH[14,1] 32.053 0.466 31.159 32.046 32.986
beta3_pH[15,1] 31.274 0.623 30.093 31.260 32.574
beta3_pH[16,1] 32.197 1.034 30.509 32.086 34.606
beta3_pH[1,2] 29.480 8.146 18.481 27.870 44.455
beta3_pH[2,2] 26.968 7.548 18.420 24.299 44.350
beta3_pH[3,2] 37.554 7.423 19.377 41.329 44.078
beta3_pH[4,2] 31.374 8.258 18.850 29.035 44.156
beta3_pH[5,2] 30.892 8.124 18.460 30.574 45.265
beta3_pH[6,2] 32.816 6.361 18.956 35.076 44.257
beta3_pH[7,2] 27.971 7.373 18.427 26.157 44.241
beta3_pH[8,2] 27.655 7.247 18.272 25.992 43.843
beta3_pH[9,2] 35.491 9.616 18.760 39.525 45.713
beta3_pH[10,2] 29.490 5.682 18.841 29.873 42.822
beta3_pH[11,2] 43.400 0.174 43.119 43.383 43.764
beta3_pH[12,2] 43.203 0.269 42.653 43.171 43.764
beta3_pH[13,2] 36.044 11.063 18.451 43.774 44.022
beta3_pH[14,2] 43.356 0.222 43.057 43.312 43.855
beta3_pH[15,2] 35.697 10.921 18.361 43.266 43.754
beta3_pH[16,2] 43.509 0.188 43.167 43.504 43.863
beta3_pH[1,3] 38.903 2.157 34.130 39.533 42.573
beta3_pH[2,3] 30.754 7.455 18.600 31.270 44.713
beta3_pH[3,3] 31.779 8.573 18.484 32.122 44.491
beta3_pH[4,3] 28.716 7.772 18.390 27.200 44.746
beta3_pH[5,3] 26.611 6.602 18.270 25.071 42.681
beta3_pH[6,3] 27.598 6.615 18.737 25.768 44.491
beta3_pH[7,3] 26.534 1.007 24.940 26.374 28.874
beta3_pH[8,3] 41.493 0.288 41.012 41.488 41.956
beta3_pH[9,3] 32.959 1.470 28.568 33.446 34.217
beta3_pH[10,3] 35.254 1.425 31.897 35.944 36.831
beta3_pH[11,3] 41.804 0.775 40.159 41.855 43.146
beta3_pH[12,3] 41.748 0.370 41.037 41.759 42.462
beta3_pH[13,3] 42.587 0.825 41.111 42.561 44.333
beta3_pH[14,3] 41.093 0.543 39.972 41.109 42.096
beta3_pH[15,3] 42.513 0.624 41.257 42.563 43.594
beta3_pH[16,3] 42.879 0.708 41.308 42.972 44.029
beta0_pelagic[1] 1.930 0.431 0.755 2.082 2.418
beta0_pelagic[2] 1.363 0.281 0.529 1.432 1.713
beta0_pelagic[3] -0.031 0.708 -1.939 0.185 0.737
beta0_pelagic[4] 0.169 0.530 -1.263 0.228 1.045
beta0_pelagic[5] 0.729 1.053 -2.578 1.088 1.482
beta0_pelagic[6] 1.266 0.382 0.251 1.380 1.695
beta0_pelagic[7] 1.575 0.147 1.290 1.576 1.847
beta0_pelagic[8] 1.713 0.149 1.414 1.718 1.993
beta0_pelagic[9] 2.233 0.664 0.769 2.505 2.919
beta0_pelagic[10] 2.481 0.293 1.687 2.527 2.794
beta0_pelagic[11] 0.038 0.542 -1.384 0.118 0.734
beta0_pelagic[12] 1.687 0.142 1.403 1.685 1.968
beta0_pelagic[13] 0.312 0.197 -0.137 0.332 0.635
beta0_pelagic[14] -0.106 0.267 -0.706 -0.081 0.353
beta0_pelagic[15] -0.257 0.132 -0.517 -0.257 0.005
beta0_pelagic[16] 0.238 0.379 -0.880 0.352 0.659
beta1_pelagic[1] 0.324 0.447 0.000 0.087 1.525
beta1_pelagic[2] 0.220 0.303 0.000 0.067 1.070
beta1_pelagic[3] 1.264 1.202 0.117 0.882 5.223
beta1_pelagic[4] 1.013 0.573 0.000 0.976 2.509
beta1_pelagic[5] 0.467 1.125 0.000 0.001 4.099
beta1_pelagic[6] 0.281 0.485 0.000 0.003 1.494
beta1_pelagic[7] 2.359 10.561 0.000 0.001 26.994
beta1_pelagic[8] 0.119 0.630 0.000 0.001 0.749
beta1_pelagic[9] 0.593 0.826 0.000 0.068 2.402
beta1_pelagic[10] 0.112 0.385 0.000 0.001 1.173
beta1_pelagic[11] 3.625 1.252 2.194 3.204 6.558
beta1_pelagic[12] 2.795 0.284 2.236 2.802 3.350
beta1_pelagic[13] 2.898 0.665 1.851 2.825 4.484
beta1_pelagic[14] 4.327 1.041 2.834 4.145 6.652
beta1_pelagic[15] 2.926 0.251 2.432 2.925 3.404
beta1_pelagic[16] 3.825 1.289 2.704 3.293 7.498
beta2_pelagic[1] 1.534 2.719 -3.791 1.071 7.822
beta2_pelagic[2] 1.313 2.293 -2.950 0.880 6.976
beta2_pelagic[3] 1.493 2.121 0.034 0.656 7.389
beta2_pelagic[4] 1.747 2.165 0.061 1.044 7.565
beta2_pelagic[5] 0.318 4.253 -7.574 0.252 8.856
beta2_pelagic[6] 1.338 3.944 -7.079 1.357 9.192
beta2_pelagic[7] 0.148 4.378 -8.768 0.231 8.917
beta2_pelagic[8] 0.533 4.101 -7.733 0.469 8.929
beta2_pelagic[9] 1.430 3.779 -6.894 1.293 8.827
beta2_pelagic[10] 0.636 4.131 -8.080 0.775 8.732
beta2_pelagic[11] 1.545 2.308 0.102 0.282 7.988
beta2_pelagic[12] 4.756 2.463 1.424 4.259 10.783
beta2_pelagic[13] 0.694 0.847 0.194 0.472 2.527
beta2_pelagic[14] 0.313 0.132 0.160 0.285 0.619
beta2_pelagic[15] 4.829 2.449 1.457 4.387 10.853
beta2_pelagic[16] 3.200 2.949 0.143 2.697 9.874
beta3_pelagic[1] 27.102 7.364 18.485 24.382 44.205
beta3_pelagic[2] 28.790 8.061 18.405 26.793 44.947
beta3_pelagic[3] 29.505 5.101 19.605 29.579 42.285
beta3_pelagic[4] 25.559 3.736 19.933 25.246 37.162
beta3_pelagic[5] 31.871 9.237 18.552 30.771 45.976
beta3_pelagic[6] 30.499 7.292 18.637 30.038 44.739
beta3_pelagic[7] 28.797 8.268 18.450 27.355 44.748
beta3_pelagic[8] 29.611 7.932 18.521 28.188 44.878
beta3_pelagic[9] 29.370 6.706 18.756 27.860 44.025
beta3_pelagic[10] 29.262 8.111 18.316 27.984 44.911
beta3_pelagic[11] 42.139 2.095 36.698 42.900 45.439
beta3_pelagic[12] 43.456 0.235 43.030 43.447 43.903
beta3_pelagic[13] 42.719 1.222 40.289 42.687 45.290
beta3_pelagic[14] 42.345 1.730 38.954 42.297 45.544
beta3_pelagic[15] 43.170 0.229 42.620 43.185 43.586
beta3_pelagic[16] 43.218 0.809 41.574 43.201 45.553
mu_beta0_pelagic[1] 0.805 0.897 -1.166 0.838 2.557
mu_beta0_pelagic[2] 1.630 0.550 0.187 1.687 2.546
mu_beta0_pelagic[3] 0.308 0.501 -0.763 0.330 1.235
tau_beta0_pelagic[1] 1.171 2.992 0.056 0.542 5.742
tau_beta0_pelagic[2] 2.493 4.474 0.126 1.550 10.002
tau_beta0_pelagic[3] 1.500 1.177 0.179 1.207 4.747
beta0_yellow[1] -0.544 0.200 -0.985 -0.520 -0.242
beta0_yellow[2] 0.429 0.316 -0.606 0.491 0.772
beta0_yellow[3] -0.338 0.262 -1.029 -0.308 0.022
beta0_yellow[4] 0.730 0.345 -0.269 0.818 1.167
beta0_yellow[5] -1.236 0.409 -2.055 -1.234 -0.458
beta0_yellow[6] 0.272 0.213 -0.142 0.267 0.700
beta0_yellow[7] 0.845 0.609 -1.148 1.022 1.342
beta0_yellow[8] 0.611 0.729 -1.378 0.909 1.271
beta0_yellow[9] -0.158 0.348 -0.823 -0.143 0.419
beta0_yellow[10] 0.233 0.152 -0.061 0.232 0.525
beta0_yellow[11] -2.006 0.404 -2.811 -2.010 -1.203
beta0_yellow[12] -3.629 0.417 -4.518 -3.605 -2.865
beta0_yellow[13] -3.633 0.461 -4.621 -3.606 -2.828
beta0_yellow[14] -2.188 0.478 -3.106 -2.198 -1.230
beta0_yellow[15] -2.835 0.382 -3.621 -2.836 -2.124
beta0_yellow[16] -2.419 0.436 -3.217 -2.428 -1.529
beta1_yellow[1] 0.530 0.791 0.000 0.287 2.275
beta1_yellow[2] 1.244 0.692 0.595 1.067 3.466
beta1_yellow[3] 0.724 0.483 0.094 0.667 1.859
beta1_yellow[4] 1.726 1.025 0.701 1.360 4.729
beta1_yellow[5] 3.003 1.229 1.357 2.867 5.413
beta1_yellow[6] 2.266 0.352 1.592 2.269 2.931
beta1_yellow[7] 6.784 8.355 0.474 3.914 34.729
beta1_yellow[8] 2.281 2.057 0.022 1.926 8.690
beta1_yellow[9] 1.653 0.634 0.861 1.601 2.864
beta1_yellow[10] 2.398 0.477 1.566 2.374 3.400
beta1_yellow[11] 2.132 0.415 1.294 2.138 2.966
beta1_yellow[12] 2.427 0.423 1.634 2.406 3.330
beta1_yellow[13] 2.792 0.443 2.021 2.761 3.770
beta1_yellow[14] 2.246 0.475 1.320 2.251 3.199
beta1_yellow[15] 2.111 0.382 1.390 2.105 2.891
beta1_yellow[16] 2.187 0.434 1.324 2.196 3.005
beta2_yellow[1] -2.451 2.963 -9.618 -1.854 2.669
beta2_yellow[2] -2.731 2.643 -9.465 -1.955 -0.078
beta2_yellow[3] -2.944 2.797 -10.182 -2.167 -0.072
beta2_yellow[4] -1.595 2.291 -8.735 -0.557 -0.078
beta2_yellow[5] -4.370 2.860 -11.168 -3.835 -0.634
beta2_yellow[6] 3.604 2.231 0.956 3.016 9.226
beta2_yellow[7] -3.834 3.959 -11.317 -3.966 5.474
beta2_yellow[8] -1.755 4.134 -10.185 -1.647 6.896
beta2_yellow[9] 3.658 2.590 0.169 3.337 9.645
beta2_yellow[10] -4.019 2.568 -10.831 -3.309 -0.955
beta2_yellow[11] -3.761 2.826 -8.252 -3.687 3.618
beta2_yellow[12] -4.563 2.234 -9.747 -4.159 -1.433
beta2_yellow[13] -4.431 1.847 -8.721 -4.225 -1.639
beta2_yellow[14] -4.589 2.391 -10.214 -4.221 -0.939
beta2_yellow[15] -4.085 2.215 -9.521 -3.632 -1.070
beta2_yellow[16] -4.881 2.530 -11.597 -4.397 -1.459
beta3_yellow[1] 27.482 7.753 18.353 24.973 44.565
beta3_yellow[2] 28.982 2.668 21.968 28.874 33.824
beta3_yellow[3] 33.009 3.490 23.916 32.990 41.116
beta3_yellow[4] 28.770 4.288 19.659 28.139 37.027
beta3_yellow[5] 33.388 1.396 30.645 33.437 35.532
beta3_yellow[6] 39.671 0.547 38.719 39.645 40.910
beta3_yellow[7] 20.885 3.079 18.502 20.096 29.667
beta3_yellow[8] 24.987 5.790 18.305 23.805 42.569
beta3_yellow[9] 37.484 2.534 31.342 37.554 42.630
beta3_yellow[10] 29.332 0.545 28.044 29.396 30.152
beta3_yellow[11] 44.350 4.006 28.499 45.410 45.972
beta3_yellow[12] 43.316 0.399 42.534 43.287 44.119
beta3_yellow[13] 44.887 0.381 44.022 44.955 45.528
beta3_yellow[14] 44.286 0.899 43.192 44.272 45.793
beta3_yellow[15] 45.189 0.516 44.144 45.171 45.961
beta3_yellow[16] 44.543 0.639 43.382 44.537 45.845
mu_beta0_yellow[1] 0.060 0.561 -1.092 0.053 1.217
mu_beta0_yellow[2] 0.071 0.490 -0.955 0.096 1.026
mu_beta0_yellow[3] -2.475 0.603 -3.411 -2.561 -1.008
tau_beta0_yellow[1] 2.244 4.559 0.098 1.250 9.150
tau_beta0_yellow[2] 1.340 1.412 0.162 0.968 4.776
tau_beta0_yellow[3] 1.693 2.567 0.100 1.037 6.646
beta0_black[1] 0.030 0.189 -0.331 0.027 0.395
beta0_black[2] 1.865 0.178 1.492 1.882 2.145
beta0_black[3] 1.272 0.161 0.903 1.287 1.543
beta0_black[4] 2.115 0.359 1.252 2.144 2.602
beta0_black[5] 1.533 1.875 -2.997 1.609 5.488
beta0_black[6] 1.605 1.941 -2.778 1.658 5.732
beta0_black[7] 1.542 1.906 -2.825 1.616 5.516
beta0_black[8] 1.259 0.231 0.803 1.267 1.696
beta0_black[9] 2.409 0.267 1.877 2.419 2.899
beta0_black[10] 1.463 0.132 1.192 1.465 1.712
beta0_black[11] 3.420 0.192 3.040 3.434 3.746
beta0_black[12] 4.484 0.185 4.124 4.489 4.842
beta0_black[13] -0.095 0.223 -0.536 -0.096 0.333
beta0_black[14] 2.131 0.552 0.632 2.247 2.787
beta0_black[15] 1.156 0.292 0.458 1.201 1.543
beta0_black[16] 4.008 0.709 1.739 4.212 4.560
beta2_black[1] 2.201 3.458 -6.075 2.238 8.903
beta2_black[2] -0.155 3.156 -6.188 -0.351 6.454
beta2_black[3] 0.249 4.049 -8.088 0.368 8.532
beta2_black[4] -1.228 3.069 -7.288 -1.293 6.153
beta2_black[5] -0.100 4.200 -8.338 -0.194 8.418
beta2_black[6] -0.047 4.148 -8.084 -0.157 8.260
beta2_black[7] -0.092 4.102 -8.350 -0.083 8.207
beta2_black[8] -0.203 4.193 -8.391 -0.345 8.227
beta2_black[9] -0.196 4.249 -8.852 -0.272 8.293
beta2_black[10] 0.068 4.006 -7.562 -0.108 7.883
beta2_black[11] -2.465 1.720 -6.233 -2.710 0.175
beta2_black[12] -2.996 1.926 -8.166 -2.580 -0.597
beta2_black[13] -2.498 1.833 -7.488 -2.048 -0.489
beta2_black[14] -1.745 1.674 -6.346 -1.255 -0.093
beta2_black[15] -2.355 2.336 -7.932 -2.055 1.454
beta2_black[16] -1.728 2.733 -7.760 -1.730 3.725
beta3_black[1] 37.427 7.422 19.391 41.226 43.548
beta3_black[2] 30.260 8.096 18.457 29.664 45.039
beta3_black[3] 29.802 7.911 18.346 29.381 45.082
beta3_black[4] 31.827 5.802 19.132 32.599 43.257
beta3_black[5] 30.055 7.878 18.450 29.245 44.827
beta3_black[6] 30.041 7.803 18.577 29.117 44.794
beta3_black[7] 30.034 7.911 18.344 28.849 44.788
beta3_black[8] 30.000 7.997 18.459 28.961 44.776
beta3_black[9] 30.164 8.008 18.503 29.161 44.910
beta3_black[10] 29.931 7.917 18.602 28.854 44.971
beta3_black[11] 29.633 6.833 18.589 29.560 43.232
beta3_black[12] 32.793 1.126 30.391 32.950 33.878
beta3_black[13] 39.308 0.729 37.653 39.386 40.459
beta3_black[14] 38.107 3.783 27.487 38.717 44.741
beta3_black[15] 31.662 7.933 18.599 31.439 45.080
beta3_black[16] 28.110 7.402 18.368 26.477 44.597
beta4_black[1] -0.265 0.191 -0.627 -0.262 0.107
beta4_black[2] 0.246 0.176 -0.098 0.246 0.601
beta4_black[3] -0.932 0.184 -1.290 -0.930 -0.572
beta4_black[4] 0.506 0.224 0.063 0.506 0.954
beta4_black[5] 0.136 2.506 -5.281 0.134 5.347
beta4_black[6] 0.259 2.629 -4.128 0.162 5.202
beta4_black[7] 0.179 2.326 -4.178 0.086 4.877
beta4_black[8] -0.685 0.364 -1.433 -0.676 0.004
beta4_black[9] 1.431 0.998 -0.147 1.297 3.711
beta4_black[10] 0.027 0.182 -0.339 0.029 0.381
beta4_black[11] -0.690 0.208 -1.101 -0.686 -0.293
beta4_black[12] 0.305 0.332 -0.323 0.302 0.989
beta4_black[13] -1.192 0.212 -1.602 -1.193 -0.790
beta4_black[14] -0.126 0.229 -0.555 -0.130 0.334
beta4_black[15] -0.886 0.209 -1.292 -0.886 -0.471
beta4_black[16] -0.596 0.230 -1.044 -0.594 -0.152
mu_beta0_black[1] 1.224 0.826 -0.606 1.263 2.760
mu_beta0_black[2] 1.581 0.881 -0.477 1.635 3.352
mu_beta0_black[3] 2.295 0.975 0.142 2.348 4.104
tau_beta0_black[1] 0.834 0.822 0.062 0.590 3.054
tau_beta0_black[2] 2.189 4.959 0.060 0.897 11.116
tau_beta0_black[3] 0.261 0.179 0.052 0.221 0.716
beta0_dsr[11] -2.909 0.275 -3.476 -2.899 -2.391
beta0_dsr[12] 4.516 0.278 3.973 4.511 5.066
beta0_dsr[13] -1.356 0.368 -2.033 -1.337 -0.781
beta0_dsr[14] -3.700 0.493 -4.658 -3.691 -2.773
beta0_dsr[15] -1.922 0.269 -2.450 -1.918 -1.395
beta0_dsr[16] -2.991 0.351 -3.680 -2.989 -2.289
beta1_dsr[11] 4.845 0.294 4.276 4.842 5.432
beta1_dsr[12] 6.088 5.360 2.273 4.987 15.709
beta1_dsr[13] 2.872 0.427 2.305 2.838 3.562
beta1_dsr[14] 6.361 0.521 5.349 6.349 7.370
beta1_dsr[15] 3.311 0.278 2.758 3.311 3.851
beta1_dsr[16] 5.816 0.367 5.106 5.813 6.551
beta2_dsr[11] -8.013 2.201 -13.132 -7.662 -4.689
beta2_dsr[12] -7.051 2.588 -12.698 -6.884 -2.351
beta2_dsr[13] -6.353 2.746 -12.320 -6.284 -0.981
beta2_dsr[14] -6.019 2.634 -11.412 -5.946 -1.808
beta2_dsr[15] -7.675 2.307 -12.964 -7.398 -3.915
beta2_dsr[16] -7.862 2.309 -13.233 -7.509 -4.351
beta3_dsr[11] 43.489 0.145 43.225 43.486 43.766
beta3_dsr[12] 34.000 0.728 32.151 34.136 34.813
beta3_dsr[13] 43.250 0.331 42.845 43.191 43.861
beta3_dsr[14] 43.346 0.221 43.083 43.284 43.888
beta3_dsr[15] 43.509 0.182 43.173 43.507 43.851
beta3_dsr[16] 43.438 0.156 43.174 43.426 43.757
beta4_dsr[11] 0.582 0.211 0.163 0.575 1.017
beta4_dsr[12] 0.243 0.454 -0.644 0.245 1.169
beta4_dsr[13] -0.170 0.212 -0.596 -0.167 0.238
beta4_dsr[14] 0.150 0.243 -0.330 0.151 0.620
beta4_dsr[15] 0.731 0.208 0.323 0.729 1.147
beta4_dsr[16] 0.132 0.225 -0.305 0.135 0.576
beta0_slope[11] -1.940 0.162 -2.263 -1.940 -1.631
beta0_slope[12] -4.653 0.258 -5.178 -4.649 -4.163
beta0_slope[13] -1.351 0.197 -1.771 -1.339 -1.002
beta0_slope[14] -2.645 0.179 -2.994 -2.645 -2.303
beta0_slope[15] -1.391 0.161 -1.709 -1.392 -1.060
beta0_slope[16] -2.732 0.169 -3.061 -2.729 -2.403
beta1_slope[11] 4.591 0.299 4.018 4.587 5.192
beta1_slope[12] 5.002 0.516 4.001 5.005 6.083
beta1_slope[13] 2.895 0.474 2.209 2.844 3.986
beta1_slope[14] 6.515 0.564 5.456 6.492 7.652
beta1_slope[15] 3.056 0.275 2.522 3.057 3.597
beta1_slope[16] 5.370 0.391 4.615 5.364 6.159
beta2_slope[11] 8.115 2.353 4.492 7.767 13.731
beta2_slope[12] 7.238 2.456 2.727 7.029 12.765
beta2_slope[13] 6.049 2.867 0.471 6.172 11.745
beta2_slope[14] 6.631 2.485 2.429 6.432 12.013
beta2_slope[15] 7.603 2.397 3.692 7.256 13.317
beta2_slope[16] 7.659 2.275 4.046 7.329 13.025
beta3_slope[11] 43.474 0.151 43.197 43.473 43.763
beta3_slope[12] 43.411 0.225 43.077 43.382 43.867
beta3_slope[13] 43.626 0.413 42.926 43.712 44.230
beta3_slope[14] 43.311 0.163 43.095 43.271 43.725
beta3_slope[15] 43.508 0.197 43.147 43.509 43.877
beta3_slope[16] 43.460 0.165 43.172 43.449 43.792
beta4_slope[11] -0.566 0.212 -0.993 -0.572 -0.141
beta4_slope[12] -1.405 0.658 -2.896 -1.326 -0.355
beta4_slope[13] 0.069 0.219 -0.365 0.066 0.503
beta4_slope[14] -0.171 0.258 -0.663 -0.172 0.345
beta4_slope[15] -0.705 0.209 -1.123 -0.702 -0.300
beta4_slope[16] -0.179 0.234 -0.631 -0.182 0.279
sigma_H[1] 0.201 0.053 0.101 0.197 0.312
sigma_H[2] 0.170 0.030 0.119 0.168 0.233
sigma_H[3] 0.198 0.042 0.124 0.195 0.287
sigma_H[4] 0.417 0.077 0.290 0.408 0.588
sigma_H[5] 0.993 0.213 0.607 0.978 1.451
sigma_H[6] 0.397 0.203 0.028 0.391 0.828
sigma_H[7] 0.302 0.062 0.204 0.293 0.457
sigma_H[8] 0.419 0.091 0.287 0.406 0.616
sigma_H[9] 0.529 0.125 0.329 0.514 0.809
sigma_H[10] 0.215 0.041 0.144 0.213 0.300
sigma_H[11] 0.276 0.046 0.199 0.271 0.377
sigma_H[12] 0.438 0.166 0.209 0.410 0.774
sigma_H[13] 0.214 0.037 0.149 0.211 0.297
sigma_H[14] 0.509 0.091 0.352 0.503 0.705
sigma_H[15] 0.245 0.041 0.177 0.241 0.340
sigma_H[16] 0.225 0.043 0.153 0.221 0.323
lambda_H[1] 3.157 4.342 0.154 1.809 14.407
lambda_H[2] 8.247 7.806 0.815 6.028 29.433
lambda_H[3] 6.394 9.557 0.320 3.262 30.570
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 3.932 8.140 0.034 1.120 27.130
lambda_H[6] 7.510 15.715 0.009 1.094 46.751
lambda_H[7] 0.013 0.009 0.002 0.011 0.037
lambda_H[8] 8.261 10.614 0.117 4.572 36.532
lambda_H[9] 0.015 0.010 0.003 0.012 0.041
lambda_H[10] 0.320 0.561 0.036 0.202 1.176
lambda_H[11] 0.263 0.377 0.011 0.126 1.202
lambda_H[12] 4.709 6.143 0.204 2.650 20.653
lambda_H[13] 3.551 3.232 0.225 2.630 12.559
lambda_H[14] 3.415 4.136 0.214 2.053 14.713
lambda_H[15] 0.027 0.071 0.003 0.017 0.101
lambda_H[16] 0.812 1.167 0.048 0.425 3.801
mu_lambda_H[1] 4.369 1.857 1.290 4.170 8.446
mu_lambda_H[2] 3.870 1.917 0.660 3.728 7.786
mu_lambda_H[3] 3.500 1.835 0.733 3.218 7.609
sigma_lambda_H[1] 8.739 4.272 2.178 8.103 18.468
sigma_lambda_H[2] 8.385 4.603 1.131 7.762 18.110
sigma_lambda_H[3] 6.249 3.932 0.902 5.444 15.812
beta_H[1,1] 6.893 1.077 4.346 7.055 8.496
beta_H[2,1] 9.881 0.499 8.785 9.915 10.787
beta_H[3,1] 8.024 0.745 6.236 8.105 9.284
beta_H[4,1] 9.092 7.756 -6.995 9.272 24.356
beta_H[5,1] 0.156 2.272 -4.399 0.328 3.996
beta_H[6,1] 3.176 3.980 -6.804 4.606 7.596
beta_H[7,1] 0.352 5.874 -12.461 0.772 10.754
beta_H[8,1] 1.316 3.510 -2.306 1.208 3.559
beta_H[9,1] 12.918 5.706 1.662 12.887 24.203
beta_H[10,1] 7.103 1.713 3.374 7.199 10.385
beta_H[11,1] 5.090 3.520 -2.871 5.825 9.907
beta_H[12,1] 2.637 1.056 0.890 2.540 5.009
beta_H[13,1] 9.032 0.890 7.224 9.106 10.413
beta_H[14,1] 2.184 1.060 0.014 2.203 4.219
beta_H[15,1] -6.080 3.761 -12.725 -6.407 2.077
beta_H[16,1] 3.428 2.610 -0.738 3.091 9.535
beta_H[1,2] 7.903 0.247 7.414 7.913 8.371
beta_H[2,2] 10.024 0.136 9.756 10.024 10.294
beta_H[3,2] 8.947 0.200 8.568 8.949 9.339
beta_H[4,2] 3.590 1.497 0.799 3.541 6.662
beta_H[5,2] 1.944 0.942 0.048 1.967 3.685
beta_H[6,2] 5.784 1.047 3.248 5.959 7.416
beta_H[7,2] 2.700 1.132 0.698 2.620 5.015
beta_H[8,2] 2.999 1.033 1.278 3.116 4.212
beta_H[9,2] 3.529 1.141 1.281 3.510 5.798
beta_H[10,2] 8.193 0.342 7.498 8.193 8.852
beta_H[11,2] 9.772 0.631 8.840 9.670 11.182
beta_H[12,2] 3.945 0.358 3.278 3.922 4.686
beta_H[13,2] 9.124 0.251 8.666 9.112 9.637
beta_H[14,2] 4.014 0.364 3.297 4.011 4.751
beta_H[15,2] 11.347 0.680 9.929 11.391 12.576
beta_H[16,2] 4.533 0.799 3.001 4.526 6.172
beta_H[1,3] 8.476 0.238 8.055 8.463 8.963
beta_H[2,3] 10.067 0.115 9.845 10.067 10.307
beta_H[3,3] 9.616 0.166 9.287 9.612 9.962
beta_H[4,3] -2.476 0.908 -4.289 -2.451 -0.770
beta_H[5,3] 3.817 0.595 2.576 3.835 4.915
beta_H[6,3] 8.016 1.177 6.393 7.657 10.592
beta_H[7,3] -2.764 0.701 -4.105 -2.764 -1.344
beta_H[8,3] 5.251 0.478 4.672 5.191 6.159
beta_H[9,3] -2.855 0.754 -4.312 -2.835 -1.410
beta_H[10,3] 8.694 0.276 8.151 8.698 9.245
beta_H[11,3] 8.551 0.287 7.925 8.582 9.045
beta_H[12,3] 5.252 0.317 4.508 5.290 5.764
beta_H[13,3] 8.854 0.178 8.480 8.856 9.190
beta_H[14,3] 5.711 0.276 5.095 5.738 6.189
beta_H[15,3] 10.377 0.313 9.768 10.367 10.993
beta_H[16,3] 6.253 0.600 4.941 6.314 7.248
beta_H[1,4] 8.274 0.181 7.885 8.284 8.601
beta_H[2,4] 10.129 0.121 9.874 10.137 10.345
beta_H[3,4] 10.117 0.162 9.770 10.129 10.398
beta_H[4,4] 11.801 0.466 10.883 11.807 12.694
beta_H[5,4] 5.456 0.730 4.293 5.362 7.106
beta_H[6,4] 7.097 0.935 4.999 7.369 8.374
beta_H[7,4] 8.231 0.350 7.509 8.234 8.909
beta_H[8,4] 6.720 0.241 6.278 6.735 7.138
beta_H[9,4] 7.210 0.489 6.240 7.205 8.204
beta_H[10,4] 7.759 0.236 7.323 7.751 8.254
beta_H[11,4] 9.382 0.204 8.988 9.381 9.778
beta_H[12,4] 7.139 0.209 6.720 7.142 7.562
beta_H[13,4] 9.053 0.144 8.761 9.056 9.327
beta_H[14,4] 7.722 0.225 7.282 7.720 8.182
beta_H[15,4] 9.464 0.236 8.997 9.460 9.942
beta_H[16,4] 9.342 0.239 8.910 9.333 9.826
beta_H[1,5] 8.987 0.145 8.699 8.988 9.266
beta_H[2,5] 10.782 0.092 10.610 10.780 10.976
beta_H[3,5] 10.919 0.173 10.607 10.907 11.284
beta_H[4,5] 8.400 0.468 7.506 8.391 9.335
beta_H[5,5] 5.403 0.570 4.049 5.466 6.363
beta_H[6,5] 8.820 0.623 7.891 8.680 10.273
beta_H[7,5] 6.800 0.336 6.161 6.791 7.481
beta_H[8,5] 8.219 0.203 7.861 8.206 8.627
beta_H[9,5] 8.202 0.480 7.257 8.201 9.139
beta_H[10,5] 10.082 0.228 9.607 10.089 10.512
beta_H[11,5] 11.518 0.227 11.066 11.521 11.956
beta_H[12,5] 8.495 0.200 8.123 8.490 8.903
beta_H[13,5] 10.013 0.133 9.758 10.014 10.276
beta_H[14,5] 9.196 0.230 8.770 9.184 9.679
beta_H[15,5] 11.169 0.251 10.668 11.171 11.652
beta_H[16,5] 9.917 0.179 9.543 9.923 10.255
beta_H[1,6] 10.182 0.189 9.851 10.164 10.615
beta_H[2,6] 11.517 0.106 11.313 11.516 11.727
beta_H[3,6] 10.808 0.161 10.461 10.816 11.099
beta_H[4,6] 12.850 0.835 11.160 12.866 14.456
beta_H[5,6] 5.887 0.608 4.688 5.883 7.041
beta_H[6,6] 8.782 0.698 6.992 8.922 9.740
beta_H[7,6] 9.827 0.560 8.739 9.827 10.934
beta_H[8,6] 9.516 0.260 9.031 9.527 9.962
beta_H[9,6] 8.481 0.800 6.961 8.484 10.069
beta_H[10,6] 9.516 0.312 8.838 9.542 10.064
beta_H[11,6] 10.816 0.346 10.090 10.838 11.456
beta_H[12,6] 9.368 0.257 8.863 9.358 9.918
beta_H[13,6] 11.048 0.161 10.758 11.036 11.397
beta_H[14,6] 9.822 0.294 9.252 9.818 10.394
beta_H[15,6] 10.839 0.438 9.982 10.838 11.704
beta_H[16,6] 10.538 0.239 10.029 10.545 10.984
beta_H[1,7] 10.881 0.862 8.700 10.991 12.276
beta_H[2,7] 12.218 0.427 11.323 12.222 13.064
beta_H[3,7] 10.547 0.662 9.027 10.633 11.635
beta_H[4,7] 2.612 4.298 -5.824 2.496 11.255
beta_H[5,7] 6.357 1.752 2.932 6.349 10.173
beta_H[6,7] 9.643 2.418 5.098 9.531 15.659
beta_H[7,7] 10.755 2.787 5.324 10.757 16.157
beta_H[8,7] 10.919 0.934 9.342 10.894 12.497
beta_H[9,7] 4.447 4.138 -3.830 4.451 12.554
beta_H[10,7] 9.837 1.419 7.275 9.753 12.977
beta_H[11,7] 10.990 1.690 7.811 10.889 14.581
beta_H[12,7] 10.005 0.935 7.961 10.083 11.553
beta_H[13,7] 11.662 0.747 9.733 11.757 12.833
beta_H[14,7] 10.394 0.936 8.430 10.456 12.010
beta_H[15,7] 11.984 2.265 7.524 11.977 16.366
beta_H[16,7] 12.285 1.285 10.134 12.119 15.187
beta0_H[1] 8.858 12.854 -16.526 9.097 34.180
beta0_H[2] 10.823 6.092 -1.477 10.805 23.947
beta0_H[3] 9.930 10.160 -10.406 9.922 30.457
beta0_H[4] 11.257 182.273 -355.751 14.934 390.950
beta0_H[5] 3.915 23.120 -40.842 4.234 49.843
beta0_H[6] 7.481 51.193 -110.424 7.805 116.802
beta0_H[7] 2.972 130.201 -261.072 4.511 265.686
beta0_H[8] 6.477 30.223 -14.777 6.444 29.545
beta0_H[9] 8.394 119.030 -225.139 4.836 252.891
beta0_H[10] 8.668 31.763 -57.527 8.540 74.506
beta0_H[11] 9.437 50.095 -94.637 9.869 109.535
beta0_H[12] 6.574 11.028 -14.609 6.483 28.741
beta0_H[13] 9.724 11.970 -11.034 9.649 32.446
beta0_H[14] 6.797 11.640 -16.919 6.938 30.856
beta0_H[15] 9.740 108.260 -202.615 8.961 235.753
beta0_H[16] 7.959 25.515 -43.271 7.747 61.021